ICLR 2026 Papers

Large language models (LLMs) exhibit remarkable mathematical reasoning abilities through supervised fine-tuning (SFT) or reinforcement learning with verifiable rewards (RLVR). However, adapting them to scientific domains like molecular optimization is challenging: its datasets provide only reference molecules, lacking the reasoning traces for SFT, while its competitive objectives hinder RLVR. To address these issues, we introduce Demonstration-guided Policy Optimization (DePO). We leverage reference molecules as supervised signals to regularize the search direction while preserving the model’s reasoning capabilities. Experiments show that DePO significantly outperforms both SFT and RLVR across key molecular optimization metrics, and excels in balancing the competitive optimization objectives. DePO achieves up to 13\% improvement compared to SFT and other baseline approaches. DePO also shows generalization capabilities and inference-scaling properties.

Neural methods are transforming automated reasoning for proof assistants, yet integrating these advances into practical verification workflows remains challenging. A $\textit{hammer}$ is a tool that integrates premise selection, translation to external automatic theorem provers, and proof reconstruction into one overarching tool to automate tedious reasoning steps. We present LeanPremise, a novel neural premise selection system, and we combine it with existing translation and proof reconstruction components to create LeanHammer, the first end-to-end domain general hammer for the Lean proof assistant. Unlike existing Lean premise selectors, LeanPremise is specifically trained for use with a hammer in dependent type theory. It also dynamically adapts to user-specific contexts, enabling it to effectively recommend premises from libraries outside LeanPremise's training data as well as lemmas defined by the user locally. With comprehensive evaluations, we show that LeanPremise enables LeanHammer to solve 21\% more goals than existing premise selectors and generalizes well to diverse domains. Our work helps bridge the gap between neural retrieval and symbolic reasoning, making formal verification more accessible to researchers and practitioners.

Large reasoning models (LRMs) trained with *Reinforcement Learning with Verifiable Rewards* (RLVR) have achieved remarkable progress on complex reasoning tasks. However, RLVR heavily relies on on-policy rollout generation, whose cost grows rapidly with rollout length and model size, eventually becoming the training bottleneck. Our empirical analysis reveals that independent rollouts for the same query often share similar early steps, indicating substantial redundancy. To address this, we propose **Pros** (**P**refix **R**euse for **O**n-policy **S**ampling), a paradigm that reuses promising prefixes of historical rollouts in RLVR training. **Pros** appends these self-generated partial rollouts to the original queries to form *Augmented Queries*, which are then used as regular training inputs in subsequent iterations, thereby reducing redundant computation. To select training batch from augmented queries, **Pros** adopts a hierarchical Bayesian model to estimate their pass rates and prioritize those with the highest reward uncertainty. Experiments across diverse settings show that **Pros** consistently improves training efficiency and achieves higher accuracy than strong baselines. These results highlight **Pros** as a practical path toward scalable and compute-efficient RLVR.

We introduce _String Seed of Thought (SSoT)_, a novel prompting method for LLMs that improves _Probabilistic Instruction Following (PIF)_. We define PIF as a task requiring an LLM to select its answer from a predefined set of options, each associated with a specific probability, such that the empirical distribution of the generated answers aligns with the target distribution when prompted multiple times. While LLMs excel at tasks with single, deterministic answers, they often fail at PIF, exhibiting biases problematic for applications requiring non-deterministic behaviors, such as human-behavior simulation, content diversification, and multiplayer games. It also harms the diversity of generated responses, a crucial factor in test-time scaling, by causing the outputs to collapse into a limited set of answers. To address this, we propose SSoT, a simple prompting method that instructs an LLM to first output a random string to generate sufficient entropy. SSoT also instructs the LLM to extract randomness by manipulating this string to derive a final answer, thereby preserving diversity while adhering to specific constraints. We demonstrate that SSoT significantly improves the PIF performance of LLMs, approaching the ideal performance of a pseudo-random number generator. Notably, our experiments on NoveltyBench show SSoT's benefits extend beyond closed-set tasks to open-ended tasks by enhancing response diversity.

Previous work shows that the chain of continuous thought (continuous CoT) improves the reasoning capability of large language models (LLMs) by enabling implicit parallel thinking, and a subsequent work provided theoretical insight by showing that a two-layer transformer equipped with continuous CoT can efficiently solve directed graph reachability by maintaining a superposition of multiple reasoning traces in the continuous thought. However, it remains unclear how the superposition mechanism is naturally learned from gradient-based training methods. To fill this gap, we theoretically analyze the training dynamics of a simplified two-layer transformer on the directed graph reachability problem to unveil how the superposition mechanism emerges during training in two training stages -- (i) a *thought-generation* stage that autoregressively expands the continuous thought, and (ii) a *prediction* stage that converts the thought into the final answer. Our analysis reveals that during training using continuous thought, the index-matching logit, an important quantity which reflects the strength of the model's local search ability, will first increase and then remain bounded under mild assumptions. The bounded index-matching logit effectively balances exploration and exploitation during the reasoning process: the model will exploit local problem structures to identify plausible search traces, and assign comparable weights to multiple such traces to explore when it is uncertain about which solution is correct, which results in superposition. Our experimental results tracking the growth of logits further validate our theory.

Preference alignment has enabled large language models (LLMs) to better reflect human expectations, but current methods mostly optimize for population-level preferences, overlooking individual users. Personalization is essential, yet early approaches—such as prompt customization or fine-tuning—struggle to reason over implicit preferences, limiting real-world effectiveness. Recent “think-then-generate” methods address this by reasoning before response generation. However, they face challenges in long-form generation: their static one-shot reasoning must capture all relevant information for the full response generation, making learning difficult and limiting adaptability to evolving content. To address this issue, we propose **FlyThinker**, an efficient “think-while-generating” framework for personalized long-form generation. FlyThinker employs a separate reasoning model that generates latent token-level reasoning in parallel, which is fused into the generation model to dynamically guide response generation. This design enables reasoning and generation to run concurrently, ensuring inference efficiency. In addition, the reasoning model is designed to depend only on previous responses rather than its own prior outputs, which preserves training parallelism across different positions—allowing all reasoning tokens for training data to be produced in a single forward pass like standard LLM training, ensuring training efficiency. Extensive experiments on real-world benchmarks demonstrate that FlyThinker achieves better personalized generation while keeping training and inference efficiency.

Large Language Models (LLMs) have shown strong performance in complex reasoning tasks, especially when guided by Chain-of-Thought (CoT) prompting. However, conventional CoT reasoning in the discrete token space suffers from high computational and memory costs due to verbose intermediate steps. Recent work has explored latent reasoning in the embedding space to improve efficiency, but often at the cost of clarity and performance. In this work, we propose $\underline{Hy}$brid $\underline{Rea}$soning ($\texttt{HyRea}$), a unified framework that enables LLMs to dynamically switch between explicit (token-based) and latent (embedding-based) reasoning during inference. To train the model to make these decisions effectively, we introduce a two-stage training pipeline: (1) a supervised cold-start phase that introduces latent reasoning by replacing low-entropy CoT steps with embeddings, and (2) a reinforcement learning phase using Group Relative Policy Optimization (GRPO) to fine-tune the model’s reasoning strategy based on task-specific rewards. Experiments on mathematical reasoning benchmarks show that \texttt{HyRea} achieves significant reductions in token usage while maintaining or improving accuracy, offering an effective and scalable solution for efficient multi-step reasoning in LLMs.

Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities in mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with “I don’t know”. Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL—a novel framework that promotes concise and boundary-aware factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeek-R1-Distill-Llama-8B from 39.33% to 61.48%, while still achieving accuracy comparable to models finetuned on reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System 2 LRMs.

Large Language Models (LLMs) demonstrate remarkable capabilities in solving complicated reasoning tasks by imitating the human thinking process from human languages. However, even the most capable LLMs can still fail in tasks that are simple for humans. To understand the gap, we construct structural causal models of next-token predictors in human languages. As language is primarily a tool for humans to share knowledge instead of thinking, modeling human thinking from languages can integrate language expression biases into LLMs. More specifically, we show that LLMs can fail to understand implicit expressions -- expression patterns occur less frequently during training. Consequently, LLMs can easily overlook critical information when biased by implicit expressions. We verify our theoretical claims with carefully constructed realistic datasets containing implicit expressions. Furthermore, we also propose a prompt-level intervention to instruct LLMs to carefully expand and focus on all the expressions available. The empirical success of the prompt-level intervention across 11 tasks and 4 representative LLMs, along with the improvements over general reasoning tasks, reaffirms our findings.

Competitive programming has emerged as a critical benchmark for evaluating the reasoning and coding capabilities of Large Language Models (LLMs). Despite impressive progress on existing benchmarks, we argue that current evaluations overstate model proficiency, masking a substantial gap between LLMs and elite human programmers. This gap arises from two key limitations: insufficient difficulty and scope of benchmark problems, and evaluation bias from low-quality test cases. To address these shortcomings, we present **AetherCode**, a new benchmark that draws problems from premier programming competitions such as IOI and ICPC, offering broader coverage and higher difficulty. AetherCode further incorporates comprehensive, expert-validated test suites built through a hybrid of automated generation and human curation, ensuring rigorous and reliable assessment. By combining challenging problem design with robust evaluation, AetherCode provides a more faithful measure of LLM capabilities and sets a new standard for future research in code reasoning.

We propose FlowRL: matching the full reward distribution via flow balancing instead of solely maximizing rewards in large language model (LLM) reinforcement learning (RL). Recent advanced reasoning models adopt reward-maximizing methods (e.g., PPO and GRPO), which tend to over-optimize dominant reward signals while neglecting less frequent but valid reasoning paths, thus reducing diversity. In contrast, we transform scalar rewards into a normalized target distribution using a learnable partition function, and then minimize the reverse KL divergence between the policy and the target distribution. We implement this idea as a flow-balanced optimization method that promotes diverse exploration and generalizable reasoning trajectories. We conduct experiments on both math and code reasoning tasks: FlowRL achieves a significant average improvement of $10.0\%$ over GRPO and $5.1\%$ over PPO on math benchmarks, and performs consistently better on code reasoning tasks. These results highlight reward distribution-matching as a key step toward efficient exploration and diverse reasoning in LLM reinforcement learning.

Alpha mining seeks to identify predictive alpha factors that generate excess returns beyond the market from a vast and noisy search space; however, existing approaches struggle to facilitate the systematic evolution of alphas. Traditional methods, such as genetic programming, are unable to interpret human natural-language instructions and often fail to extract valuable insights from unsuccessful attempts, leading to low interpretability and inefficient exploration. Analogously, without mechanisms for systematic evolution, e.g., long-term planning and reflection, multi-agent approaches may easily fall into repetitive evolutionary routines, thereby failing to realize efficient self-evolution. To overcome these limitations, we introduce **AlphaAgentEvo**, a self-evolving Agentic Reinforcement Learning (ARL) framework for alpha mining, which moves alpha mining beyond the brittle “search–backtest–restart” cycle toward a continuous trajectory of evolution. Instructed by a hierarchical reward function, our agent engages in self-exploration of the search space, progressively learning basic requirements (e.g., valid tool calls) and then harder objectives (e.g., continuous performance improvements). Through this process, the agent acquires advanced behaviors such as long-horizon planning and reflective reasoning, which enable it to actively react to the underlying state (e.g., market regime shifting) and realize a self-evolving agent, taking a step toward more principled and scalable alpha mining. Extensive experiments demonstrate that AlphaAgentEvo achieves more efficient alpha evolution and generates more diverse and transferable alphas, consistently surpassing a wide range of baselines. Notably, with only 4B parameters, it outperforms LLM-driven evolution methods configured with state-of-the-art close-source reasoning models, highlighting the promise of ARL for next-generation alpha mining.

Large language models (LLMs) increasingly rely on Chain-of-Thought (CoT) prompting to improve problem-solving and provide seemingly transparent explanations. However, growing evidence shows that CoT often fail to faithfully represent the underlying reasoning process, raising concerns about their reliability in high-risk applications. Although prior studies have focused on mechanism-level analyses showing that CoTs can be unfaithful, they leave open the practical challenge of deciding whether a specific trajectory is faithful to the internal reasoning of the model. To address this gap, we introduce FaithCoT-Bench, a unified benchmark for instance-level CoT unfaithfulness detection. Our framework establishes a rigorous task formulation that formulates unfaithfulness detection as a discriminative decision problem, and provides FINE-CoT (Faithfulness instance evaluation for Chain-of-Thought), an expert-annotated collection of over 1,000 trajectories generated by four representative LLMs across four domains, including more than 300 unfaithful instances with fine-grained causes and step-level evidence. We further conduct a systematic evaluation of eleven representative detection methods spanning counterfactual, logit-based, and LLM-as-judge paradigms, deriving empirical insights that clarify the strengths and weaknesses of existing approaches and reveal the increased challenges of detection in knowledge-intensive domains and with more advanced models. To the best of our knowledge, FaithCoT-Bench establishes the first comprehensive benchmark for instance-level CoT faithfulness, setting a solid basis for future research toward more interpretable and trustworthy reasoning in LLMs.

Unified multimodal understanding and generation models recently have achieve significant improvement in image generation capability, yet a large gap remains in instruction following and detail preservation compared to systems that tightly couple comprehension with generation such as GPT-4o. Motivated by recent advances in interleaving reasoning, we explore whether such reasoning can further improve text-to-image (T2I) generation. We introduce Interleaving Reasoning Generation (IRG), a framework that alternates between text-based thinking and image synthesis: the model first produces a text-based thinking to guide an initial image, then reflects on the result to refine fine-grained details, visual quality, and aesthetics while preserving semantics. To train IRG effectively, we propose Interleaving Reasoning Generation Learning (IRGL), which targets two sub-goals: (1) strengthening the initial think-and-generate stage to establish core content and base quality, and (2) enabling high-quality textual reflection and faithful implementation of those refinements in a subsequent image. We curate IRGL-300K, a 300K-scale dataset organized into six decomposed learning modes that jointly cover learning text-based thinking, and full thinking–image trajectories. Starting from a unified foundation model that natively emits interleaved text–image outputs, our two-stage training first builds robust thinking and reflection, then efficiently tunes the IRG pipeline in the full thinking–image trajectory data. Extensive experiments show SoTA performance, yielding absolute gains of 5–10 points on GenEval, WISE, TIIF, GenAI-Bench, and OneIG-EN, alongside substantial improvements in visual quality and fine-grained fidelity. As an early exploration, our results demonstrate that interleaving reasoning is a powerful paradigm for advancing T2I.

Vision-Language Models (VLMs) in remote sensing often fail at complex analytical tasks, a limitation stemming from their end-to-end training paradigm that bypasses crucial reasoning steps and leads to unverifiable outputs. To address this limitation, we introduce the Perceptually-Grounded Geospatial Chain-of-Thought (Geo-CoT), a framework that models remote sensing analysis as a verifiable, multi-step process. We instill this analytical process through a two-stage alignment strategy, leveraging Geo-CoT380k, the first large-scale dataset of structured Geo-CoT rationales. This strategy first employs supervised fine-tuning (SFT) to instill the foundational cognitive architecture, then leverages Group Reward Policy Optimization (GRPO) to refine the model’s reasoning policy towards factual correctness. The resulting model, RSThinker, outputs both a final answer and its justifying, verifiable analytical trace. This capability yields dominant performance, significantly outperforming state-of-the-art models across a comprehensive range of tasks. The public release of our Geo-CoT380k dataset and RSThinker model upon publication serves as a concrete pathway from opaque perception towards structured, verifiable reasoning for Earth Observation.

In this work, we propose ***R**einforced **F**unctional **T**oken **T**uning* (RFTT), a novel reinforced fine-tuning framework that empowers Large Language Models (LLMs) with learn-to-reason capabilities. Unlike prior prompt-driven reasoning efforts, RFTT embeds a rich set of learnable functional tokens (*e.g.*, \<analyze\>, \<verify\>, \<refine\>) directly into the model vocabulary, enabling chain-of-thought construction with diverse human-like reasoning behaviors. Specifically, RFTT comprises two phases: (1) supervised fine-tuning performs prompt-driven tree search to obtain self-generated training data annotated with functional tokens, which warms up the model to learn these tokens for initial reasoning capability; and (2) online reinforcement learning further allows the model to explore diverse reasoning pathways through functional token sampling without relying on prompts, thereby facilitating effective self-improvement for functional reasoning. Extensive experiments demonstrate the superiority of the proposed RFTT on mathematical benchmarks and highlight its strong generalization capability to other general domains. Moreover, the performance of RFTT exhibits consistent gains with increased test-time computation through additional search rollouts. Our code and dataset are available at anonymous url.

Any entity in the visual world can be hierarchically grouped based on shared characteristics and mapped to fine-grained sub-categories. While Multi-modal Large Language Models (MLLMs) achieve strong performance on coarse-grained visual tasks, they often struggle with Fine-Grained Visual Recognition (FGVR). Adapting general-purpose MLLMs to FGVR typically requires large amounts of annotated data, which is costly to obtain, leaving a substantial performance gap compared to contrastive CLIP models dedicated for discriminative tasks. Moreover, MLLMs tend to overfit to seen sub-categories and generalize poorly to unseen ones. To address these challenges, we propose Fine-R1, an MLLM tailored for FGVR through an R1-style training framework: (1) Chain-of-Thought Supervised Fine-tuning, where we construct a high-quality FGVR CoT dataset with rationales of "visual analysis, candidate sub-categories, comparison, and prediction”, transition the model into a strong open-world classifier; and (2) Triplet Augmented Policy Optimization, where Intra-class Augmentation mixes trajectories from anchor and positive images within the same category to improve robustness to intra-class variance, while Inter-class Augmentation maximizes the response distinction conditioned on images across sub-categories to enhance discriminative ability. With only 4-shot training, Fine-R1 outperforms existing general MLLMs, reasoning MLLMs, and even contrastive CLIP models in identifying both seen and unseen sub-categories, showing promise in working in knowledge-intensive domains where gathering expert annotations for all sub-categories is arduous. Code is available at [https://github.com/PKU-ICST-MIPL/FineR1_ICLR2026](https://github.com/PKU-ICST-MIPL/FineR1\_ICLR2026).

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful framework for improving the reasoning abilities of Large Language Models (LLMs). However, current methods such as GRPO rely only on problems where the model responses to the same input differ in correctness, while ignoring those where all responses receive the same reward — so-called zero-variance prompts. In this work, we argue that such prompts are not useless but can, in fact, provide meaningful feedback for policy optimization. To this end, we introduce Reinforcement Learning with Zero-Variance Prompts (RL-ZVP), a novel algorithm that extract learning signals from zero-variance prompts. RL-ZVP directly rewards correctness and penalizes errors even without contrasting responses, modulating feedback with token-level characteristics to preserve informative, nuanced signals. Across six math reasoning benchmarks, RL-ZVP achieves significant improvements of up to 8.61 points in accuracy and 7.77 points in pass rate over GRPO, while consistently outperforming other baselines that filter out zero-variance prompts. These results highlight the untapped potential of learning from zero-variance prompts in RLVR.

Reasoning is not just about solving problems---it is also about evaluating which problems are worth solving at all. Evaluations of artificial intelligence (AI) systems primarily focused on problem solving, historically by studying how models play games such as chess and Go. In this paper, we advocate for a new paradigm that assesses AI systems' evaluation of games. First, we introduce a formalism for evaluating such evaluations. We then leverage a large-scale dataset of over 100 novel board games and over 450 human judgments to compare evaluations produced by modern language and reasoning models against those of people and symbolic computational agents. We consider two kinds of evaluative queries: assessing the payoff (or fairness) and the funness of games. These queries span two dimensions relevant to the design of evaluations of AI evaluations: how complex a query is to compute and how difficult a query is to quantify. Our results show that reasoning models are generally more aligned to people in their evaluations of games than non-reasoning language models. However, we observe a non-monotonic relationship: as models get closer to game-theoretic optimal, their fit to human data weakens. We also observe more "jaggedness" across models for assessing funness, in line with the greater difficulty of quantifying this query. Across queries and games, reasoning models show highly variable and unpredictable resource usage when assessing queries, pointing to the importance of imbuing more resource-rational meta-reasoning in language and reasoning models.